Timeline for Beauville-Laszlo for schemes
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2019 at 18:19 | comment | added | Will Sawin | @PiotrAchinger Since the idea of working in the Raynaud setup and not another one was yours, that might be a complete answer to the question... | |
| Sep 15, 2019 at 18:11 | comment | added | Piotr Achinger | The paper "Berkovich spaces and tubular descent" by Ben-Bassat and Temkin seems relevant, though they work in the Berkovich setup. From the abstract: "We consider an algebraic variety $X$ together with the choice of a subvariety $Z$. We show that any coherent sheaf on $X$ can be constructed out of a coherent sheaf on the formal neighborhood of $Z$, a coherent sheaf on the complement of $Z$ , and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space $W$ which we define." | |
| Sep 15, 2019 at 18:03 | comment | added | prochet | My issue is the same as Achinger, their definition does not make sense already for $\widehat{X}$, because $\mathcal{O}_{S}[[t]]$ is not quasi-coherent. Does it hold if we go in the world of rigid spaces? | |
| Sep 15, 2019 at 16:00 | comment | added | Piotr Achinger | I am baffled by their definition of $\widehat{X}$ as a scheme, as completion does not commute with localization. After all, this is why formal schemes were invented. In any case it seems more natural to replace $\widehat{X}$ with the respective formal scheme, but then $\widehat{X}^*$ should be a rigid space a'la Raynaud... | |
| Sep 15, 2019 at 15:00 | history | answered | Will Sawin | CC BY-SA 4.0 |